Textbook Notes (368,317)
Mathematics (241)
MATH 135 (23)
Mike Eden (3)
Chapter

# Integer Propositions

5 Pages
98 Views

School
Department
Mathematics
Course
MATH 135
Professor
Mike Eden
Semester
Fall

Description
List of All PropositionsSeptember25111140 PMTransitivity of Divisibility TDProofSince ab there exists an integer r so that rab 1Since bc there exists an integer s so that sbc 2Substituting ra for b in the previous equation we get sr ac 3Since sr is an integer ac4TopDivisibility of Integer Combinations DICSince ab there exists an integer k such that bka1Since ac there exists an integer l such that cla2Let x and y be any integers3Now bxcykaxlayakxly 4Since kxly Z it follows that abxcy5TopBounds By Divisibility BBDSince ab there exists an integer q so that bqa 1Since b 6 0 q 6 0 2But if q 6 0 q 1 3But then bqaqaa4TopDivision Algorithm DATopGreatest Common Denominator With Remainders GCD WR MATH 135 Page 1
More Less

Related notes for MATH 135
Me

OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.

Get notes from the top students in your class.

Request Course
Submit